Unfortunately there only way out is to spend a bit of cash. Although a certain level of noise is acceptable - noise to signal ratio.
But if there is too much noise at low levels then I'd be looking for other stuff first.
I'd check for a gain setting on the back of those monitors though. I'm not familiar with them at all, but there could be something. Getting noise with nothing conected isn't great at all. Even gains or room compensation switches shouldn't cause an audible hiss though (specially with nothing conected).
Sound card noise has many variables indeed. I had trouble with a network card once. And my SCSI card always causes noise when it's accessing the sampler. Power suplys, poorly placed cables ect...Pull the sucker appart and put it back together is an idea - vary the positions of cards.
I know you said the levels were mid-way on your mixer, but how about your preamps? If the onboard pre's are cranking then they could put out a bit of noise. Mmmm, but you did say the Tascam was quiet....
How is your grounding? Does your house have properly grounded outlets. Here in Japan I had to run a cable out the window to ground my gear.
Other than this (and everything else that has been brought up), I can't think of anything else.
Hope you get it sorted.
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